Artículo
Amster, P.; Kwong, M.K.; Rogers, C. "A neumann boundary value problem in two-ion electro-diffusion with unequal valencies" (2012) Discrete and Continuous Dynamical Systems - Series B. 17(7):2299-2311
Este artículo es de Acceso Abierto y puede ser descargado en su versión final desde nuestro repositorio
Consulte la política de Acceso Abierto del editor
Abstract:
In prior work, a series of two-point boundary value problems have been investigated for a steady state two-ion electro-diffusion model system in which the sum of the valencies ν + and ν - is zero. In that case, reduction is obtained to the canonical Painlevé II equation for the scaled electric field. Here, a physically important Neumann boundary value problem in the generic case when ν ++ν - = 0 is investigated. The problem is novel in that the model equation for the electric field involves yet to be determined boundary values of the solution. A reduction of the Neumann boundary value problem in terms of elliptic functions is obtained for privileged valency ratios. A topological index argument is used to establish the existence of a solution in the general case, under the assumption ν ++ν - ≤ 0.
Registro:
| Documento: | Artículo |
| Título: | A neumann boundary value problem in two-ion electro-diffusion with unequal valencies |
| Autor: | Amster, P.; Kwong, M.K.; Rogers, C. |
| Filiación: | Departamento de Matemática, FCEyN, Universidad de Buenos Aires and CONICET, Ciudad Universitaria Pab. I, 1428 Buenos Aires, Argentina Department of Applied Mathematics, Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong Australian Research Council Centre, School of Mathematics and Statistics, University of New South Wales, Sydney, Australia |
| Palabras clave: | Neumann boundary conditions; Topological index; Two-ion electro-diffusion; Unequal valencies |
| Año: | 2012 |
| Volumen: | 17 |
| Número: | 7 |
| Página de inicio: | 2299 |
| Página de fin: | 2311 |
| DOI: | http://dx.doi.org/10.3934/dcdsb.2012.17.2299 |
| Título revista: | Discrete and Continuous Dynamical Systems - Series B |
| Título revista abreviado: | Discrete Contin. Dyn. Syst. Ser. B |
| ISSN: | 15313492 |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_15313492_v17_n7_p2299_Amster.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15313492_v17_n7_p2299_Amster |
Referencias:
- Nernst, W., Zur Kinetik der in Lösung befindlichen Körper: I Theorie der Diffusion (1882) Z. Phys. Chem., 2, pp. 613-637
- Planck, M., Über die erregung von elektricität und wärme in electrolyten (1890) Ann. Phys. Chem., 39, pp. 161-186
- Cole, K.S., (1968) Membranes, Ions and Impulses, , University of California Press, Berkeley
- Schwarz, T.L., (1971) Biophysics and Physiology of Excitable Membranes, , (ed. W. J. Adelman, Jr.), Van Rostrand, New York
- O'M Bokris, J., Reddy, A.K.N., (1971) Modern Electrochemistry, , Plenum, New York
- Leuchtag, H.R., A family of differential equations arising from multi-ion electrodiffusion (1981) J. Mathematical Phys., 22, pp. 1317-1320
- Conte, R., Rogers, C., Schief, W.K., Painlevé structure of a multi-ion electrodiffusion system (2007) J. Phys. A, 40, pp. F1031-F1040
- Thompson, H.B., Existence for two-point boundary value problems in two-ion electrodiffusion (1994) J. Math. Anal. Appl, 184, pp. 82-94
- Grafov, B.M., Chernenko, A.A., Theory of the passage of a constant current through a solution of a binary electrolyte (1962) Dokl. Akad. Nauk. SSR, 146, pp. 135-138
- Bass, L., Electrical structures of interfaces in steady electrolysis (1964) Trans. Faraday Soc., 60, pp. 1655-1663
- Kudryashov, N.A., The second Painlevé equation as a model for the electric field in a semiconductor (1997) Physics Letters, Section A: General, Atomic and Solid State Physics, 233 (4-6), pp. 397-400. , PII S0375960197005458
- Rogers, C., Bassom, A., Schief, W.K., On a Painlevé II model in steady electrolysis: Application of a Bäcklund transformation (1999) J. Math. Anal. Appl., 240, pp. 367-381
- Bass, L., Nimmo, J., Rogers, C., Schief, W.K., Enhanced structures of interfaces: A Painlevé II model (2010) Proc. Roy. Soc. London Ser. A Math. Phys. Eng. Sci., 466, pp. 2117-2136
- Bass, L., Irreversible interactions between metals and electrolytes (1964) Proc. Roy. Soc. London A, 277, pp. 125-136
- Amster, P., Kwong, M.K., Rogers, C., On a Neumann boundary value problem for Painlevé II in two-ion electro-diffusion Nonlinear Analysis, Theory, Methods and Applications, , in press
- De Coster, C., Habets, P., Upper and lower solutions in the theory of ODE boundary value problems: Classical and recent results (1996) Nonlinear Analysis and Boundary Value Problems for ODEs, pp. 1-78. , CISM Courses and Lectures 371 Springer, Vienna
Citas:
---------- APA ----------
Amster, P., Kwong, M.K. & Rogers, C. (2012) . A neumann boundary value problem in two-ion electro-diffusion with unequal valencies. Discrete and Continuous Dynamical Systems - Series B, 17(7), 2299-2311.http://dx.doi.org/10.3934/dcdsb.2012.17.2299
---------- CHICAGO ----------
Amster, P., Kwong, M.K., Rogers, C. "A neumann boundary value problem in two-ion electro-diffusion with unequal valencies" . Discrete and Continuous Dynamical Systems - Series B 17, no. 7 (2012) : 2299-2311.http://dx.doi.org/10.3934/dcdsb.2012.17.2299
---------- MLA ----------
Amster, P., Kwong, M.K., Rogers, C. "A neumann boundary value problem in two-ion electro-diffusion with unequal valencies" . Discrete and Continuous Dynamical Systems - Series B, vol. 17, no. 7, 2012, pp. 2299-2311.http://dx.doi.org/10.3934/dcdsb.2012.17.2299
---------- VANCOUVER ----------
Amster, P., Kwong, M.K., Rogers, C. A neumann boundary value problem in two-ion electro-diffusion with unequal valencies. Discrete Contin. Dyn. Syst. Ser. B. 2012;17(7):2299-2311.http://dx.doi.org/10.3934/dcdsb.2012.17.2299
